WASHINGTON — President Barack Obama had lunch Wednesday with Republican leaders of the House of Representatives, and the federal budget was first on the menu.

Just days before he unveils his proposed federal budget for the next fiscal year, he and the top Republicans said they agreed in general on the need to cut federal spending and the budget deficit, as well as approve free trade agreements with South Korea, Colombia and Panama.

But they didn't talk specifics — the White House refused to share budget details with Congress before the president unveils it on Monday. And recent votes in the House suggest that even if the Republican leaders can forge a spending agreement with Obama, they could have trouble getting it past their own party.

"We did have a fairly robust conversation about the need for all of us to work together to send a signal that we're serious about cutting spending. We had agreement on that," House Majority Leader Eric Cantor, R-Va., said outside the White House.

"I guess the particulars and the details will be where the disagreements may rise."

"We looked at places where we could work together: jobs and cutting government spending," added Rep. Kevin McCarthy, R-Calif., the House majority whip. "It was a beginning and a start and we look forward."

White House Press Secretary Robert Gibbs, who didn't sit in on the lunch, called it very constructive.

"They agreed on cutting spending and reducing our deficits," he said. "They discussed areas such as trade where they can work together . . . . Obviously, reducing the deficit and growing the economy were things the president most discussed."

House Speaker John Boehner, R-Ohio, said afterward that he's committed to holding House votes to approve a free trade agreement with South Korea that Obama's team negotiated late last year. White House aides said the administration would send specific trade-agreement language soon, and hoped to send Congress free trade agreements with Colombia and Panama later this year.

As Boehner, Cantor and McCarthy dined at the White House, they faced questions back at the Capitol about how much they can deliver.

The 87 Republican freshmen, along with many veteran conservative members, want GOP leaders to push harder for their conservative agenda.

This week, they've made their voices heard — and at times embarrassed their leaders.

Most notably, 26 Republicans voted Tuesday night against an extension of the Patriot Act, the controversial George W. Bush-era anti-terrorism law. GOP leaders were so confident the bill would pass that they tried to push it through under a special procedure requiring a two-thirds majority.

Democrats split on the extension as well — 67 for and 122 against.

But the inability of the Republicans to deliver all of their votes suggested problems ahead for party discipline in the House, where new conservatives campaigned on the memory of seeing fellow Republicans cave to pressure from former Majority Leader Tom DeLay of Texas in delivering votes for big spending.

Hours earlier Tuesday, House Republican leaders suffered another setback: They delayed a long-scheduled vote on legislation to extend Trade Adjustment Assistance, which offers aid and training to people whose jobs are lost or whose hours are reduced because of foreign competition.

The popular program is set to expire Saturday, and usually draws support from both parties. Conservatives have been wary, indicating they want to see progress on the long-delayed trade agreements with Colombia, Panama and South Korea.

House Republican leaders endured another defeat Wednesday, as an effort to deny U.S. funding to the United Nations failed to pass. The measure needed a two-thirds majority and fell 27 votes short, with two Republicans joining 167 Democrats in opposition. The bill, pushed by GOP leaders, said the U.S. should get back $179 million it's overpaid to a U.N. fund. Until the money is returned, the legislation said, the U.S. was to withhold $179 million in U.N. payments.

Lurking on the horizon is an even more explosive issue: Spending. Conservatives are disappointed that House Budget Committee Chairman Paul Ryan, R-Wis., has proposed cutting only $32 billion in fiscal 2011. The government's spending authority expires on March 4.

The Republican Study Committee, the leading House conservative group, has proposed $80 billion in savings this year and $2.5 trillion over 10 years. The House is expected to vote on several of these proposals next week.

Among the committee's ideas: Eliminating or dramatically reducing subsidies for the Corporation for Public Broadcasting, the Legal Services Corp., the National Endowment for the Arts and Amtrak; and funding for weatherization grants, the presidential campaign fund and intercity and high-speed rail projects.

House leaders say they welcome efforts to make more cuts. "There has been a lot of talk on our side that members want to cut even further, and most of us welcome that talk and will be supporting yet even further cuts," Cantor said.